Persona: Vallejo Rodríguez, José Antonio
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Vallejo Rodríguez
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Publicación Wave functions of the Hydrogen atom in the momentum representation(IOPscience, 2023-03-03) Kirchbach, Mariana; Vallejo Rodríguez, José Antonio; https://orcid.org/0000-0002-4264-3296We construct the integral transform passing from the space representation to the radial momentum representation for the Hydrogen atom. The resulting wave functions are explicitly given in terms of complex finite expansions of Gegenbauer functions of the first and second kind, or in terms of (elementary) trigonometric functions. We show their symmetry under the (SO4) group, and their equivalence with those of Lombardi and Ogilvie (2020 Chem. Phys. 538 110886)Publicación Closed stable orbits in a strongly coupled resonant Wilberforce pendulum(Sage Journals, 2021-01-30) Avendaño Camacho, Misael; Torres Manotas, Alejandra; Vallejo Rodríguez, José AntonioWe prove the existence of closed stable orbits in a strongly coupled Wilberforce pendulum, for the case of a 1:2 resonance, by using techniques of singular geometric reduction combined with the more classical averaging method of Moser.Publicación Color confinement at the boundary of the conformally compactified AdS5(Springer Nature, 2021-09-27) Kirchbach, Mariana; Popov, Todor; Vallejo Rodríguez, José AntonioThe topology of closed manifolds forces interacting charges to appear in pairs. We take advantage of this property in the setting of the conformal boundary of AdS5 spacetime, topologically equivalent to the closed manifold S1 × S3, by considering the coupling of two massless opposite charges on it. Taking the interaction potential as the analog of Coulomb interaction (derived from a fundamental solution of the S3 Laplace-Beltrami operator), a conformal S1 × S3 metric deformation is proposed, such that free motion on the deformed metric is equivalent to motion on the round metric in the presence of the interaction potential. We give explicit expressions for the generators of the conformal algebra in the representation induced by the metric deformation. By identifying the charge as the color degree of freedom in QCD, and the two charges system as a quark-anti-quark system, we argue that the associated conformal wave operator equation could provide a realistic quantum mechanical description of the simplest QCD system, the mesons. Finally, we discuss the possibility of employing the compactification radius, R, as another scale along ΛQCD, by means of which, upon reparametrizing Q2c2 as (Q2c2+ħ2c2/R2), a perturbative treatment of processes in the infrared could be approached.Publicación Potentials on the conformally compactified Minkowski spacetime and their application to quark deconfinement(World Scientific, 2024-05-15) Kirchbach, Mariana; Vallejo Rodríguez, José Antonio; https://orcid.org/0000-0002-4264-3296We study a class of conformal metric deformations in the quasi-radial coordinate parameterizing the 3-sphere in the conformally compactified Minkowski spacetime S1 ×S3. Prior to reduction of the associated Laplace-Beltrami operators to a Schr¨odinger form, a corresponding class of exactly solvable potentials (each one containing a scalar and a gradient term) is found. In particular, the scalar piece of these potentials can be exactly or quasi-exactly solvable, and among them we find the finite range confining trigonometric potentials of P¨oschl-Teller, Scarf and Rosen-Morse. As an application of the results developed in the paper, the large compactification radius limit of the interaction described by some of these potentials is studied, and this regime is shown to be relevant to a quantum mechanical quark deconfinement mechanism.Publicación Symplectic scalar curvature on supermanifolds(World Scientific, 2023-04-08) Hernández-Amador, Rosalía G.; Vallejo Rodríguez, José Antonio; Vorobiev, YuIn this paper, we study the notion of symplectic scalar curvature on the supermanifold over an ordinary Fedosov manifold whose structural sheaf is that of differential forms. In this purely geometric context, we introduce two families of odd super-Fedosov structures, the first one is very general and uses a graded symmetric connection, leading to a vanishing odd symplectic scalar curvature, while the second one is based on a graded non-symmetric connection and has a nontrivial odd symplectic scalar curvature. As a simple example of the second case, we determine that curvature when the base Fedosov manifold is the torus.